Problem: What do the following two equations represent? $2x-y = 4$ $2x+4y = 5$
Explanation: Putting the first equation in $y = mx + b$ form gives: $2x-y = 4$ $-y = -2x+4$ $y = 2x - 4$ Putting the second equation in $y = mx + b$ form gives: $2x+4y = 5$ $4y = -2x+5$ $y = -\dfrac{1}{2}x + \dfrac{5}{4}$ The slopes are negative inverses of each other, so the lines are perpendicular.